Blend the pineapple, ice, vodka, liqueur and sugar until smooth and frothy in a blender.
Pour into chilled glasses and garnish with pineapple and paper umbrellas.
To make vanilla-flavored vodka, place 3 whole vanilla beans in a 750 ml bottle of plain vodka. Place the bottle in a cool dark place for at least 10 days to allow the vanilla to infuse the vodka. Open the bottle occasionally during the infusion time.
For a non-alcoholic version, blend one 16-ounce bag of frozen pineapple, 1 cup ginger ale, 1 cup fresh orange juice, 1 cup coconut milk and 2 teaspoons vanilla extract, if desired, until smooth in a blender.